Abstract

We examine two isomorphisms between afine Hecke algebras of type A associated with parameters q⁻¹, t⁻¹ and q, t. One of them maps the non-symmetric Macdonald polynomials E_η(x;q⁻¹,t⁻¹) onto E_η(x;q,t), while the other maps them onto non-symmetric analogues of the multivariable Al-Salam & Carlitz polynomials. Using the properties of E_η(x;q⁻¹ ,t⁻¹), the corresponding properties of these latter polynomials can then be elucidated.

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